KdV-type equations admit solitary wave solutions, which means that the solutions often contain localized structures. This makes adaptivity very appealing in efficient numerical simulations, which is another aim of this work.
In particular, this paper continues our line of research [1]}, [2]}, [3]}, [4]}, [5]} on the development of adaptive multiresolution DG methods. The adaptivity in our proposed schemes is realized through the hierarchical polynomial spaces and multiresolution analysis (MRA), which has built in error indicators. By further incorporating the sparse tensor product in 2D space, adaptive multiresolution UWDG schemes for the ZK equation are capable of capturing solitary waves efficiently. Two classes of multiwavelets are employed in our schemes to attain MRA. First, the Alperts orthonormal multiwavelets are adopted as the DG basis functions [6]}, and then the interpolatory multiwavelets [7]} are introduced to deal with the nonlinear terms in the scheme.
